Optimal aggregate sustainability assessment of total and selected factors of industrial processes

Vector space theory has been applied successfully to sustainability assessment of industrial processes. Processes sharing similar factors of production are represented by vectors in the space generated by the factors. The length of the vectors measures their sustainability index. This procedure leads to an ordered inequality among the set of processes. The present work shows first that each process vector is an optimal solution based on the projection theorem of optimization theory. The best option is usually the process with the smallest index in this hierarchy. It may occur though that this process is not the most sustainable in terms of particular environmental factors. For instance, the least index may be mainly due to smaller resource factors needed for production and yet has larger emissions of greenhouse gases and toxic materials. The decision-maker may choose a more environmentally sustainable process whose overall aggregate index of total factors is not the least index in the hierarchy. The set of critical factors define a subspace within the whole factor space. Another aim of the present work consists also in finding out the optimal process vectors on the selected subspaces by employing the same procedure based on the projection theorem. The decision-maker may then compare the resultant subspace hierarchies to the one from all factors. The method is then applied to automobile fender designs and food supply chain, whose factors in both cases are obtained from life cycle assessments.